In the brackets the first product is, according to Euler’s theorem on homogeneous functions, equal to λ⁢U→λnormal-→U\lambda\vec{U}. The second product can be written as Ux⁢∂⁡r→∂⁡x+Uy⁢∂⁡r→∂⁡y+Uz⁢∂⁡r→∂⁡zsubscriptUxnormal-→rxsubscriptUynormal-→rysubscriptUznormal-→rzU_{x}\frac{\partial\vec{r}}{\partial x}+U_{y}\frac{\partial\vec{r}}{\partial y%
}+U_{z}\frac{\partial\vec{r}}{\partial z}, which is Ux⁢i→+Uy⁢j→+Uz⁢k→subscriptUxnormal-→isubscriptUynormal-→jsubscriptUznormal-→kU_{x}\vec{i}+U_{y}\vec{j}+U_{z}\vec{k}, i.e. U→normal-→U\vec{U}. The third product is, due to the sodenoidalness, equal to 0⁢r→=0→0normal-→rnormal-→00\vec{r}=\vec{0}. The last product equals to 3⁢U→3normal-→U3\vec{U} (see the first formula for position vector). Thus we get the result